The first thing to do is download the software. A link can be found on Microsoft's website here.
The box that contains the text "Download Now" downloads the Windows Essentials 2012 installer. There are options for other languages and earlier versions in the "Other download options" link. Windows Essentials 2011 is not available, however, because of a bug that caused security issues. You can learn more about that here.
After the download is complete, open the installer. This installer is for all Windows Essentials 2012 programs, so you also have the option of installing Messenger, Writer, and other programs if you wish. Follow through the prompts and the installer will install the software you selected. Once installed, restart your computer to finish the job.
When you open Movie Maker for the first time, a window will pop up with the terms and conditions of using the software. Read through them and click accept. Movie Maker will then open and you are ready to begin your project.